Add QM energy in Python (#333)

* Implement QM energy in Python.

* Add QM energy in Python to book.

Author: berquist

contents/quantum_systems/code/python/energy.py

@@ -0,0 +1,17 @@
+import numpy as np
+
+
+def calculate_energy(wfc, H_k, H_r, dx):
+    """Calculate the energy <Psi|H|Psi>."""
+    # Creating momentum conjugate wavefunctions
+    wfc_k = np.fft.fft(wfc)
+    wfc_c = np.conj(wfc)
+
+    # Finding the momentum and real-space energy terms
+    energy_k = 0.5 * wfc_c * np.fft.ifft((H_k ** 2) * wfc_k)
+    energy_r = wfc_c * H_r * wfc
+
+    # Integrating over all space
+    energy_final = sum(energy_k + energy_r).real
+
+    return energy_final * dx

contents/quantum_systems/quantum_systems.md

@@ -227,6 +227,8 @@ This ultimately looks like this:
 {% method %}
 {% sample lang="jl" %}
 [import, lang:"julia"](code/julia/energy.jl)
+{% sample lang="py" %}
+[import:4-17, lang:"python"](code/python/energy.py)
 {% endmethod %}
 
 This calculation will be used in many different simulations of quantum systems to check our results.